If log_(2) P = x, log_(2) Q = y, and log_(2) R = z, write in term of x, y, z. log_(2) (√(R) )/(y=PQ^(3) )

Question

If
`log_(2)` P = x,
`log_(2)` Q = y, and
`log_(2)` R = z, write in term of x, y, z.


`log_(2) (√(R) )/(y=PQ^(3) )`

Answer 1

The answer is (1/2)z - x - 3y

Explanation:

∵
`log_(2)P=x`

∵
`log_(2)Q=y`

∵
`log_(2)R=z`

∵
`log_(2)\frac{R^{(1)/(2)}}{(P)(Q^(3))}`

∴
`log_(2)(R)^{(1)/(2)}-log_(2)P-log_(2)(Q^(3))`

∴
`(1)/(2)log_(2)R-log_(2)P-3log_(2)Q`

∴
`(1)/(2)z-x-3y`